Group in which every normal subgroup is finite or has finite index
This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism
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A group in which every normal subgroup is finite or has finite index is a group in which every normal subgroup satisfies one of these two conditions: either it is a finite group (and hence a finite normal subgroup), or it is a normal subgroup of finite index in the whole group.
Relation with other properties
|Property||Meaning||Proof of implication||Proof of strictness (reverse implication failure)||Intermediate notions|
|group in which every nontrivial normal subgroup has finite index|